| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime } x -4 \sqrt {y^{2}-x^{2}}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.906 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
372.370 |
|
| \begin{align*}
\left (y+{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.403 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.015 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (5\right ) &= 8 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.141 |
|
| \begin{align*}
y^{\prime } t +y&=t^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
y^{\prime }&=y \left (t y^{3}-1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{t}&=t^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.023 |
|
| \begin{align*}
5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.366 |
|
| \begin{align*}
3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.851 |
|
| \begin{align*}
y^{\prime }&=y+\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.651 |
|
| \begin{align*}
y^{\prime }&=r y-k^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.864 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.700 |
|
| \begin{align*}
y^{\prime }+3 t y&=4-4 t^{2}+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.999 |
|
| \begin{align*}
\left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.421 |
|
| \begin{align*}
1&=\left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| \begin{align*}
y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| \begin{align*}
y^{\prime } x +\left (x +1\right ) y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.613 |
|
| \begin{align*}
\frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.649 |
|
| \begin{align*}
5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
2 y y^{\prime } x +\ln \left (x \right )&=-1-y^{2} \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.956 |
|
| \begin{align*}
\left (-x +2\right ) y^{\prime }&=y+2 \left (-x +2\right )^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| \begin{align*}
y^{\prime } x&=-\frac {1}{\ln \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.732 |
|
| \begin{align*}
4 y y^{\prime } x&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.789 |
|
| \begin{align*}
y^{\prime }+y-y^{{1}/{4}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.785 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
x^{\prime }&=x+2 y+\sin \left (t \right ) \\
y^{\prime }&=-x+y-\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| \begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \begin{align*}
x^{\prime }&=x+2 y+4 \\
y^{\prime }&=-2 x+y-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x^{\prime }&=x+y+4 \\
y^{\prime }&=-2 x+\sin \left (t \right ) y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.041 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
x^{\prime }&=x-4 y+2 t \\
y^{\prime }&=x-3 y-3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{\prime }&=-x+y+1 \\
y^{\prime }&=x+y-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
x^{\prime }&=-x-4 y-4 \\
y^{\prime }&=x-y-6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\
y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
x^{\prime }&=-2 x+y-11 \\
y^{\prime }&=-5 x+4 y-35 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
x^{\prime }&=x+y-3 \\
y^{\prime }&=-x+y+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{\prime }&=-5 x+4 y-35 \\
y^{\prime }&=-2 x+y-11 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\
y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x}{4}-2 y \\
y^{\prime }&=x-\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
x^{\prime }&=-\frac {4 x}{5}+2 y \\
y^{\prime }&=-x+\frac {6 y}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-x+a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=-5 y \\
y^{\prime }&=x+a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=a x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=a x+\frac {5 y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=-x+a y \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \begin{align*}
x^{\prime }&=4 x+a y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\
v^{\prime }&=2 i-\frac {v}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{2}+y \\
y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
x^{\prime }&=-x-\frac {y}{2} \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.470 |
|